Finite element approximation of the transport of reactive solutes in porous media. part II: Error estimates for equilibrium adsorption processes
Barrett JW, Knabner P (1997)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 1997
Journal
Publisher: Society for Industrial and Applied Mathematics
Book Volume: 34
Pages Range: 455-479
Journal Issue: 2
DOI: 10.1137/S0036142993258191
Abstract
In this paper we analyze a fully practical piecewise linear finite element approximation involving numerical integration, backward Euler time discretization, and possibly regularization and relaxation of the following degenerate parabolic equation arising in a model of reactive solute transport in porous media: find u(x,t) such that u + [(u)] - δu = f in ω (0,T], u = 0 on ω (0,T] u(',0) = g(.) in ω for known data ω R, 1 ≤ d ≤ 3, f, g, and a monotonically increasing C(R) C (-,0) (0,) satisfying (0) = 0, which is only locally Hölder continuous with exponent p (0,1) at the origin; e.g., (s) [s] . This lack of Lipschitz continuity at the origin limits the regularity of the unique solution u and leads to difficulties in the finite element error analysis.
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APA:
Barrett, J.W., & Knabner, P. (1997). Finite element approximation of the transport of reactive solutes in porous media. part II: Error estimates for equilibrium adsorption processes. SIAM Journal on Numerical Analysis, 34(2), 455-479. https://doi.org/10.1137/S0036142993258191
MLA:
Barrett, John W., and Peter Knabner. "Finite element approximation of the transport of reactive solutes in porous media. part II: Error estimates for equilibrium adsorption processes." SIAM Journal on Numerical Analysis 34.2 (1997): 455-479.
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